Invariably Variables

CHAPTER 5 Invariably Variables




Statistics is a tool that helps data produce knowledge rather than confusion.


—David S. Moore and George P. McCabe1


If you were to pick up a textbook of statistics, the first chapter would invariably be about variables. It is time to start thinking about populations in terms of their variables and to incorporate this idea into your knowledge base. This lays the foundation for the actual comparison between groups. The concept of a variable is actually quite simple.



• A variable is any measurable characteristic found in each individual in a population.


Notice that this definition is very broad. There could be a limitless amount of variables (or measurable characteristics) that could potentially be identified in any population. Not all variables are important to the topic being studied. The investigators choose the variables that are most likely to be useful in determining the end result.


Variables are used to estimate population parameters. A given variable can be measured in each subject from the sample. An example is the variable “age.” Every member will have a value associated with age. These values can be used to derive a sample statistic which estimates the population parameter of average age or the standard deviation of age.



TYPES OF VARIABLES


The variables to be studied are measured in each individual of the sample that has been selected to represent the population. Numerical values are assigned to represent the value of a variable for an individual. Numbers are needed so that calculations can be made, even if the numbers do not directly represent the value of the characteristic. Take gender, for instance. Each subject is either male or female. For statistical purposes, this is often recorded as 0 for male and 1 for female (or vice versa).


Another example is the declared major in a sample of college students. This variable cannot be measured numerically but, for statistical purposes, a 1 can be assigned for Psychology, a 2 for History, a 3 for Biology, and so forth. Note that in these examples the number assigned to the variable does not represent a true numerical value. These types of variables are called categorical variables. Numbers are assigned to the subsets within the category so that a computer can perform calculations to analyze the data. These types of variables have a category key to decipher what the numerical values mean.


Other variables can be easily represented by numbers that directly reflect the value for that individual. These variables are referred to as quantitative variables. Yearly income is a good example of this. The number of dollars earned per year by an individual is directly representative of the true value of the characteristic. Another example is number of miles driven on a daily commute to work. The actual number has a real meaning; more miles driven is reflected in a higher numeric value.


You may come across other definitions for different types of variables. For instance, gender can be described as a binary or dichotomous variable, since there are only two possible values. The answers to questions with a “yes” or “no” answer (such as “Do you own a car?”) can also be considered dichotomous variables. It is not important to remember the various ways of describing variables, but you should know that different types of statistical tests are used for analyzing different types of variables.


Inherent in the definition of a variable is the fact that they do indeed vary. Different individuals will have different values of a particular variable. In some cases, the value will be only one of two possible choices, as in gender. Other variables will have several limited possibilities, such as college major. When the possible values are limited, the variables are called discrete. Variables such as annual income or serum cholesterol level, however, can have a wide variety of responses within a numeric range. These are referred to as continuous variables since there is an extensive range of possible values on a continuous scale.



SCALES OF MEASUREMENT


The different types of variables have led to another classification of variables based on the scale of measurement used to determine their value. It is not necessary to memorize these but it is useful to know that they exist. There are four classic scales of measurement:



Nominal scale. This is not really a scale at all; it is a labeling system. Categorical variables such as gender and college major are measured like this. Even though numbers are assigned to the categories, they do not have a true numerical value. They are more like the numbers on football jerseys that designate the different members of a team, without quantitative value.


Ordinal scale. In this scale, a value is given to the variable based on its place along some continuum. The relative place of the variable has some numeric meaning. For instance, we may want to measure the place of the runners in a race as they cross the finish line. First- and second-place runners may wind up being closer together than the second- and third-place runners, but this kind of scale pays attention to rank only. Using this scale, the difference between first and second place is the same as between second and third. Quality of life issues are often measured on ordinal scales. Consider a scale that measures overall contentment with regard to medical conditions, with 1 being lowest and 100 being highest. In a population of people who have undergone amputation, a subject who reports a quality of life of 95 has a higher contentment rating than someone who reports 85, who in turn is more content than someone reporting 75. However, in the scale that measures contentment we cannot say that the difference of 10 between the three individuals is equivalent.


Interval scale. This scale is used to measure continuous variables that have legitimate mathematical values. The difference between two consecutive values is consistent along any point of the scale. Many variables can be measured this way. For example, the variable yearly income is used to measure buying power. Someone who makes $60,000 per year has twice as much buying power as someone who makes $30,000 and half as much buying power as those who make $120,000 per year.


Ratio scale.

Related posts:

  1. Ethics in Medical Research
  2. Populations
  3. Measures of Disease
  4. Mathematical Principles

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Jun 18, 2016 | Posted by in BIOCHEMISTRY | Comments Off on Invariably Variables

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